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Love Thy Neighbor: Income Distribution and Housing Preferences Tin Cheuk Leung Chinese University of Hong Kong Kwok Ping Tsang Virginia Tech * May 26, 2010 Preliminary - please do not cite Abstract Do homeowners prefer living in an area with a more equal distribution of income? We answer this question by estimating a nonparametric hedonic pricing model for about 90,000 housing units transacted in Hong Kong between 2005 and 2006. We first identify a hedonic price function by locally regressing the rental price of the housing unit on its intrinsic and neighborhood characteristics, one of which is the Gini coefficient for household income of the constituency area. We then combine the estimates with a log utility function to obtain the heterogeneous preference parameters. Finally, we estimate the joint distribution of the preference parameters and demographics. We find that most homeowners have a strong distaste for inequality in their neighborhood, and the distaste increases with income and goes down with age. Counterfactual experiments show that reallocating Public Rental Housing by half can increase the welfare of homeowners by about HK$8,000 on average per year, which is equivalent to increasing the housing unit by 20 square feet or reducing the age of the unit by 5 years. * First draft: March 2010. Leung: Department of Economics, Chinese University of Hong Kong, Room 914, Esther Lee Building, Chung Chi Campus, Shatin, Hong Kong. Email: [email protected] Tsang : Department of Economics, Virginia Tech, Pamplin Hall (0316), Blacksburg, Virginia, 24061. Email: [email protected] 1

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  • Love Thy Neighbor: Income Distribution and HousingPreferences

    Tin Cheuk LeungChinese University of Hong Kong

    Kwok Ping TsangVirginia Tech∗

    May 26, 2010

    Preliminary - please do not cite


    Do homeowners prefer living in an area with a more equal distribution of income? Weanswer this question by estimating a nonparametric hedonic pricing model for about 90,000housing units transacted in Hong Kong between 2005 and 2006. We first identify a hedonicprice function by locally regressing the rental price of the housing unit on its intrinsic andneighborhood characteristics, one of which is the Gini coefficient for household income ofthe constituency area. We then combine the estimates with a log utility function to obtainthe heterogeneous preference parameters. Finally, we estimate the joint distribution of thepreference parameters and demographics. We find that most homeowners have a strongdistaste for inequality in their neighborhood, and the distaste increases with income andgoes down with age. Counterfactual experiments show that reallocating Public RentalHousing by half can increase the welfare of homeowners by about HK$8,000 on averageper year, which is equivalent to increasing the housing unit by 20 square feet or reducingthe age of the unit by 5 years.

    ∗First draft: March 2010. Leung: Department of Economics, Chinese University of Hong Kong, Room 914,Esther Lee Building, Chung Chi Campus, Shatin, Hong Kong. Email: [email protected] Tsang : Departmentof Economics, Virginia Tech, Pamplin Hall (0316), Blacksburg, Virginia, 24061. Email: [email protected]


  • 1 Introduction

    “How seldom we weigh our neighbor in the same balance with ourselves”

    Of the Imitation of Christ, Thomas à Kempis (1418)

    Do homeowners have a preference for living among neighbors with a similar income level?

    Common sense suggests that homeowners prefer income equality in the neighborhood. Despite

    the alleged snobbery of the rich towards the poor and the reciprocal jealousy of the poor towards

    the rich, people with a similar income living in the same area also creates positive externality:

    more goods and services are available catering for an income group if more people in that income

    group are living in the same area. For example, a low-income household will have a hard time

    finding a cheap fast food chain in a high-income area, and it would be difficult for a high-income

    household to find an expensive restaurant in a poor neighborhood. Recent neural science

    research has also shown that humans have social preferences to reduce inequality in outcome

    distributions (see Tricomi, Rangel, Camerer, and O’Doherty (2010)).

    In this paper we give a quantitative answer to this question by studying over 90,000 trans-

    actions in the Hong Kong housing market in 2005 and 2006. We first present a simple model

    that takes the preference of a homeowner as given, and looks at the equilibrium in the housing

    market when the homeowner prefers to live near others with a similar income level. Specifically,

    the model tells us how public housing affects the equilibrium distribution of the housing units

    and the welfare change. Since we are interested only in the implications of the distaste towards

    income inequality, our model is an ad hoc one that abstracts from other important aspects of the

    housing market. We then describe the data, and explain why two unique features of the Hong

    Kong housing market are important for our purpose. First, Hong Kong is a densely populated

    area that magnifies the impact of a neighborhood effect. Second, the public housing policy

    in Hong Kong has created substantial income inequality within small areas. Using a 3-step

    nonparametric hedonic pricing technique, we obtain the willingness to pay and preference pa-

    rameters for the characteristics the housing unit and its neighborhood. In particular, we look

    at the preference for income inequality and see how the preference changes with the demograph-

    ics. Finally, we conduct a counterfactual experiment by reallocating half of the poorest public


  • housing residents in all constituency areas in Hong Kong, and look at the welfare implications.

    To the best of our knowledge, this is the first paper that estimates the preference of res-

    idents for income inequality in the neighborhood. There is some empirical research on the

    neighborhood effect or housing externalities among residents. When there is an urban renewal

    project for some area, does the land value of the nearby area also increase? Using the American

    Housing Survey for 1985 and 1989, Ioannides (2002) finds that whether the neighbors (the 10

    nearest housing units) of an individual have house maintenance substantially affects the indi-

    vidual’s maintenance decision. That is, living in a dilapidated neighborhood discourages an

    individual to improve her housing unit, and the individual has a higher incentive to renovate

    when the neighbors’ housing units look much better. A recent paper by Rossi-Hansberg, Sarte,

    and Owens (2010) looks at the concentrated residential urban revitalization programs in Rich-

    mond, VA. A few disadvantaged neighborhoods (the impact area) are supported by the federal

    government to renovate, but with the neighborhood effects the neighborhood of the impact area

    also benefits from the program. The authors find that there is an increase in the land value of

    the neighborhood, and the effect decreases with the distance from the impact area. Our paper

    differs from the housing externalities literature that we identify the preference for a neighbor-

    hood in a hedonic pricing framework instead of the behavior induced by the neighborhood. We

    quantify the distaste of people for income inequality in the neighborhood, and we measure the

    welfare gain of reducing income inequality in the residential areas in Hong Kong.

    This paper is also related to the literature of income sorting in residential areas, at least since

    Tiebout (1956). A local government collects taxes and provide public goods, and communities

    are formed endogenously. The Tiebout model predicts income stratification across communities,

    or all people in each community have the same marginal benefit from the local public goods.

    Allowing for heterogenous preferences, Epple and Platt (1998) show that it is possible reduce

    the amount of stratification, i.e. people with the same income are not necessarily in the same

    community. Using data from the American Housing Survey, Ioannides (2004) finds that within

    small neighborhoods (same as Ioannides (2002)), there is substantial income mixing. In our

    empirical framework each homeowner takes the income distribution in the constituency area as

    given, and from the data we infer how much the homeowner is willing to pay for less income

    inequality in the area. Income distribution within constituency areas in Hong Kong are not only


  • determined by the competitive market, but are influenced by public housing policy (see Section

    2). Based on the estimated preference, we look at the welfare implications of reducing income

    inequality in the constituency areas.

    2 Why the Hong Kong Housing Market?

    Hong Kong is famous for being a densely populated city. According to the World Population

    Prospects (2008 revision), the estimate of population density in Hong Kong is 6,433 people per

    squared kilometre for the year 2010, in contrast with 33 people in the United States, 225 people

    in the United Kingdom and 336 people in Japan. Of course, Hong Kong is less populated than

    major cities in the US like Manhattan, New York (25,850 people, Census Bureau data). But

    since Hong Kong is characterized by being mountainous and high-rises, some of the residential

    areas we study can be highly populated. For example, a medium-quality high-rise of 40 floors

    usually have more than 16 housing units on each floor, and residents are forced into having

    frequent interactions with neighbors (in the elevator, or even hearing a conversation from next

    door). As a result, the existence of a neighborhood effect will be the most convincing for the

    case of Hong Kong than in the areas studied in the literature.

    As our interest is the preference for income inequality in the neighborhood and the potential

    benefit of removing inequality, we need to study residential areas with significant variations of

    income distribution. The public housing policy in Hong Kong has contributed to the substantial

    income inequality in different areas of Hong Kong.

    In 1953, a fire in Shek Kip Mei destroyed thousands of shanty homes. Since then, the

    government of Hong Kong began to construct homes for the poor. A significant portion of

    people in Hong Kong are inhabiting in public housing. According to 2006 census, 3.4 million

    people, out of 6.9 million, lived in public housing provided by the Hong Kong government. This

    is the greatest government intervention in a city renowned for its free-market principle.

    There are three main types of public housing in Hong Kong. The first type is Public Rental

    Housing estates which are the most numerous type of public housing. As of 2006, 2.1 million

    people lived in Public Rental Housing estates. Applicants’ income and total net assets value

    cannot exceed certain limits, which vary between families, the elderly and individual applicants.


  • For instance, the monthly income and total net asset limit for a two-person household are

    HK$11,660 and HK$252,000.

    The second type is the Home Ownership Scheme estates. These are subsidized-sale public

    housing estates for low-income residents. As of 2006, 1.2 million people lived in these es-

    tates. The income and asset limits are higher than that of the Public Rental Housing estates.

    The monthly income and total net asset limit for a two-person household are HK$23,000 and


    The third type is the Sandwich Class Housing Scheme estates. They were built for sale to

    the “sandwich class”, which are the lower-middle and middle-income residents not eligible for

    other public housing but have difficulties affording private housing. The flats are sold at prices

    slightly below market value (usually 70%), but with quality comparable to some middle-class

    private housing. The supply of these estates are limited. Only 48,106 people lived in these

    Sandwich Class Housing Scheme estates in 2006.

    For purpose of elections in the District Council, the government divide Hong Kong into 18

    districts. In each districts, there are several sub-districts (constituency areas). In total, there

    are 380 constituency area.

    The Census data only allows us to separately identify the demographics of the Public Rental

    Housing estates and the rest. Thus, in the analysis below, we focus to analyze on how Public

    Rental Housing estates affect Gini and welfare of homeowners in different constituency area.

    One distinct feature in the Hong Kong housing market is that public housing inhabited

    by lower-income group and private housing inhabited by higher-income group can coexist in

    the same neighborhood (or the same constituency area). While about half of the constituency

    areas (186 out of 380) do not have any Public Rental Housing estates, Figure 1 shows that the

    percentage of Public Rental Housing units in a constituency area varies evenly across the rest

    of the constituency areas.

    3 A Stylized Location Model

    Given that people have a distaste for income inequality in the neighborhood, what can we say

    about the location choice of the people? How does the introduction of public housing affect


  • Figure 1:

    Percentage of Public Rental Housing Across Constituency Areas (excluding constituency areaswithout any public rental housing)


  • the location choice? Does public housing reduce the welfare of some people? To illustrate

    the main points of this paper, in this section we present a highly stylized model that takes the

    preference of residents as given, and abstracts from many other aspects of the housing market.

    In the model, there is a unit measure of agents, i ∈ [0, 1]. Each agent is endowed with

    income w(i), with w′(i) ≥ 0, so agent 0 is the poorest and agent 1 is the wealthiest. Given w(i)

    and w(−i), agent i chooses to stay in neighborhood n, where n = 1, . . . , N . Denote the policy

    function of agent i, which will be discussed further below, as P (i| − i).

    In this model, an agent has a distaste to stay in a neighborhood in which neighbors’ incomes

    are very different from that of the agent. The utility of agent i living in neighborhood n is:

    u(i, n) = −∫ 1


    P (j| − j)[w(i)− w(j)]2


    where Sn =∫ 1

    0P (j| − j) dj.

    Agent i’s problem is to choose a neighborhood that maximizes his utility. Thus the policy

    function solves the fixed point problem below:

    P (i| − i) = arg maxku(i, k) (1)

    We have not been able to prove the existence and uniqueness of the fixed point. Thus, no

    analytical solution can be provided at the moment. Instead, we solve the fixed point numerically

    and find that the result is fairly robust.

    The set up of the numerical exercise is as follows. We have 200 home buyers and 5 locations.

    Income of each home buyer is drawn from a log-normal distribution. Income is then sorted from

    low to high, so that w(1) ≤ w(2) ≤ . . . ≤ w(200). Each home buyer chooses to locate in one of

    the 5 neighborhoods as modeled above. The solution of the problem is a 200-by-1 vector policy

    function for the 200 agents. That is, each policy function solves equation (1). To see if the result

    is robust to different income draws, we repeat the above steps 100 times. The average location

    and welfare can be interpreted as the expected location and welfare of the home buyer.

    We solve two equilibria. First, it is the free market equilibrium in which every agent is free

    to choose his neighborhood. Second, it is the public housing equilibrium in which the poorest

    50 agents are assigned to two neighborhoods.


  • Figure 2 shows the income distribution in each of the five neighborhoods in the two equilibria.

    The first column is the free market equilibrium, and the second column is the public housing

    equilibrium. There are two things to note. First, aside from the richest neighborhood, the

    incomes in all other neighborhoods are more spread in the public housing equilibrium. This

    means all but the richest agents would be worse off when there is public housing. Second, the

    income of agents living in private housing is lower in the two neighborhoods with public housing,

    which is empirically testable.

    4 Data Description

    In this paper, we use housing transaction data, provided by Economic Property Research Center,

    between 2005-06 as our main source of data.1 We then supplement this data with 2006 Hong

    Kong by-census data, available on the internet.

    4.1 Housing Transaction Data

    The housing transaction data contains many micro-aspect of each transaction, including prices,

    gross and net area, address, floor, age, number of bedrooms and living rooms, and so forth.

    This data have pros and cons compared with more conventional micro data from US Census of

    Population and Housing. On the one hand, the census data provide more detailed homeowners’

    demographic and financial information than our data. We can only use the average demographic

    information of people living in private housing in various constituency areas to proxy it. But,

    on the other hand, the home price data from the Census is self reported and is top coded at

    US$875,000. In addition, home prices are partitioned into only 23 mutually exclusive categories.

    Also, Census data only provide limited information on the home’s characteristics such as the

    number of rooms and age of the structure.

    There are 357,931 observations in the initial data. We drop observations with missing char-

    acteristics like prices, floor, area e.t.c. We then select the observations in major estates and

    building in each constituency area and merge it with census data which has the demographic

    1For studies on the Hong Kong housing market using the same dataset, see Leung, Lau, and Leong (2002)and Leung, Leong, and Wong (2006).


  • Figure 2:

    Income Distribution in Different Neighborhood (Column 1: free market equilibrium; Column2: public housing equilibrium)


  • Table 1: Data Selection in the Homes Transaction DataYear 2005 Year 2006

    Reasons for exclusion # dropped # remain # dropped # remainInitial Sample N.A. 173445 N.A. 184486Missing Floor 4097 169348 3613 180873Missing Gross Area 45072 124276 53017 127856Missing Net Area 14249 110027 15429 112427Missing Bedroom 26587 83440 27691 84736Missing Living Room 31 83409 24 84712Price = 0 1731 81678 2021 82691Price Outliers 1621 80057 1652 81039Non-major Estates/Buildings 33790 46267 38216 42823

    Table 2: Summary Statistics for Hong Kong Homes Transacted in 2005-06Year 2005 Year 2006

    Price ($HK Million) 2.46 (1.81) 2.51 (2.02)Floor 18.63 (12.77) 18.31 (12.29)Gross Area (sq ft) 713.61 (248.34) 722.07 (263.45)Net Area (sq ft) 561.94 (207.10) 572.86 (224.54)Bedrooms 2.38 (0.55) 2.40 (0.56)Living Rooms 1.87 (0.33) 1.86 (0.34)Age of Structure 12.42 (7.85) 14.07 (7.76)Swimming Pool 0.80 (0.40) 0.78 (0.41)Club House 0.54 (0.50) 0.52 (0.50)std. dev. in parenthesis. N = 46267 N = 42823

    statistics for each constituency area. This leaves us with 89090 observations. Table 1 describes

    data selection process.

    Table 2 summarizes the characteristics of the transacted housing units between 2005-2006.

    The transaction prices and the transacted housing units are reasonably similar across the two

    years, which can serve as a justification for treating the two years as the same market in the

    later analysis.

    4.2 Census Data

    The 2006 by-census data includes various demographic, social, educational, economic and house-

    hold information of each of the 380 constituency areas. Table 3 summarizes the demographic

    information of the constituency areas. The average population in a constituency area is 17,148.

    All of the variables reported in Table 3 have reasonable variation across constituency areas.

    Income inequality of a neighborhood is an important attribute for buying a home. Despite


  • Table 3: Summary Statistics of Constituency AreasMean Std. Dev. Min. Max.

    Population 17148.22 4465.66 5158 46447Median Age 39.72 3.23 26 50Median Household Income 10769.88 2959.966 7000 25000Average Household Size 3.00 0.32 2.3 4% Post Secondary Education 22.25 12.69 5 64.9Gini 0.45 0.06 0.22 0.60% Public Rental Housing 0.30 0.37 0 1N=380

    the alleged snobbery of the rich towards the poor and the reciprocal hatred of the poor towards

    the rich, people with a similar income living in the same area also creates positive externality:

    more goods and services are available catering for an income group if more people in that income

    group are living in the area. Also, as Gans (1961) points out, tension may arise from differences

    in child-rearing norms among different income groups. While “people with higher incomes and

    more education may feel that they or their children are being harmed by living among less

    advantaged neighbors. The latter are likely to feel equally negative about the ‘airs’ being put

    on by the former.”. As shown in Table 3, the gini coefficients across constituency areas vary a

    lot from 0.22 to 0.6, average at 0.45.

    5 Model

    In this section, we build a model of housing demand for households in Hong Kong between 2005

    and 2006. A home j = 1, . . . , J is a bundle of three types of characteristics: physical attributes,

    community attributes and attributes observed by consumer but not by econometricians. Physical

    attributes include the number of rooms, the age of the unit, gross and net area of the unit,

    number of bedrooms and living rooms, and dummy variables for swimming pool and club house.

    Community attributes include average demographics of persons in the constituency area, such

    as the fraction of college educated households. The unobserved attribute is modeled as a scalar


    Prices of houses are determined by the interaction of buyers and sellers in the equilibrium.

    The price function p maps housing characteristics (x, ξ) into their equilibrium prices:


  • pj = p(xj, ξj) (2)

    Households take prices as given and solve the following static utility maximization problem:

    uij = maxjui(xj, ξj, c) Subject to: pj + c ≤ yi (3)

    where c is a composite commodity, with a price normalized to $1 (pre-tax).

    Suppose the characteristic k is continuous and that j∗ is household i’s optimal choice. The

    first-order condition of equation (3) says that the marginal rate of substitution between product

    characteristics k and the composite commodity must equal to the implicit price:

    ∂ui(xj∗ ,ξj∗ ,yi−pj∗ )∂xj,k

    ∂ui(xj∗ ,ξj∗ ,yi−pj∗ )∂c

    =∂p(xj∗ , ξj∗)


    As noted by Bajari and Benkard (2005b) and Bajari and Kahn (2008), a single cross section

    observed in this data is not enough to recover a household’s utility function globally. We follow

    the literature on random coefficient discrete choice models to specify household’s utility to be:

    uij = β′i[log(xj); log(ξj)] (5)

    We allow for a rich specification of heterogeneity in tastes as we allow the marginal valuation

    of the characteristics to be household specific, since βi are household specific. Also, utility in

    equation (5) is a log-linear function of the product characteristics. The log specification allows

    product characteristics to have diminishing marginal utility.

    Most of the previous studies on differentiated product assume βi to have a parametric dis-

    tribution. In particular, they are independently and normally distributed.2 We do not impose

    any parametric distribution on βi and will estimate the distribution of new homeowners’ tastes


    In this paper, we are interested to see how distaste against income inequalities of households

    with different demographic characteristics differ. We thus model the joint distribution of the

    2See Berry, Levinsohn, and Pakes (1995), Petrin (2002), Nevo (2000), and Rossi, Allenby, and McCulloch(2005).


  • random utility coefficients, βi, and demographics.3 As discussed in Bajari and Kahn (2008), the

    lack of micro level data on household level characteristics requires an assumption of linearity

    between tastes and demographics.

    6 Estimation

    Our estimation approach involves three steps. The first two steps are similar to those used in

    Bajari and Benkard (2005a); the last step is similar to Bajari and Kahn (2008). In the first step,

    we estimate the hedonic price function p using a flexible local linear regression method described

    in Fan and Gijbels (1996) and applied in Bajari and Kahn (2005) and Bajari and Kahn (2008).

    Second, we “back out” the random utility coefficients for each household by applying first order

    conditions for optimality. Finally, we recover the joint distribution of random utility coefficients

    and household demographics. Since we only have access to demographics aggregated at the level

    of District Councils constituency areas, we follow Bajari and Kahn (2008) to estimate household

    level preferences with this aggregated data.

    6.1 First Step: Estimating the Hedonic Price Function

    We follow Fan and Gijbels (1996) to use local linear methods to estimate the hedonic flexibly.

    For a particular home j∗, we assume the hedonic price function p is locally linear and satisfies:

    pj = α0,j∗ +∑k

    αk,j∗(xj,k − xj∗,k) + ξj (6)

    We only assume the hedonic in equation (6) is locally linear, not globally linear as in a linear

    regression model. The coefficients α·,j∗ have a subscript j∗ to emphasize that they are specific

    to (xj∗ , ξj∗).

    For any j∗, 1 ≤ j∗ ≤ J , we follow Fan and Gijbels (1996) to use weighted least squares to

    estimate αj∗

    3Section 7 provides more discussion on the set up.


  • αj∗ = arg minα

    (−→p −Xα)′W(−→p −Xα) (7)

    p = [RPRICEj],X = [xj],W = diag{Kh(xj − xj∗)} (8)

    In equations (7) and (8), −→p is the vector of the owner’s equivalent rent for all homes j =

    1, . . . , J , X is a vector of regressors which correspond to the observed product characteristics

    and W is a matrix of kernel weights.

    The kernel weights in W are a function of the distance between home j∗ and j. The local

    linear regression assigns more weights to observation near j∗. As discussed in Fan and Gijbels

    (1996), local linear methods have the same asymptotic variance and a lower asymptotic bias than

    the Nadaraya-Watson estimator, whereas the Gasser-Mueller estimator has the same asymptotic

    bias and a higher asymptotic variance than local linear methods. We chose the following normal

    kernel function with a bandwidth of 3:

    K(z) =∏k

    N(zk/σ̂2) (9)

    Kh(z) = = K(z/h)/h (10)

    In equation (9), K is a product of standard normal density and σ̂2 is the standard sample

    deviation of characteristic k.

    We interpret the residual the hedonic regression from equations (7) and (8) as the unobserved

    home characteristic.

    ξj∗ = pj∗ − xj∗αj∗ (11)

    In the first step, we run a linear regression of owner equivalent rent on xj and constituency

    area fixed effect. The constituency area fixed effects absorb important attributes such as distance

    from work, air quality, crime rate and local school quality. We then subtract the constituency

    area fixed effects from the owner’s equivalent rent and estimate the local linear regressions

    described above.


  • The treatment for binary variables (e.g. the presence of a swimming pool) is different.

    Suppose the household i chooses a house j∗. Define x̂j as the observed characteristics of

    house j∗ except one of the binary variable x is set to 1, and x̄j as the same characteristics

    with the binary variable set to 0. The implicit price for the binary characteristic x is then

    p(x̂j, ξj)−p(x̄j, ξj), and if household i chooses x = 1 then βi,x > p(x̂j, ξj)−p(x̄j, ξj) and βi,x <

    p(x̂j, ξj)− p(x̄j, ξj) otherwise. That is, βi,x is not identified.

    6.2 Second Step: “Backing Out” the Random Utility Coefficients

    Due to the log utility function (5), we can calculate the random utility coefficients easily. Let

    α̂j∗,k be the estimated coefficients from the local linear regression for variable xj∗ . The coeffi-

    cients are the implicit prices faced by household i, who chooses xj∗ , in the market, and hence

    α̂j∗,k is the estimated implicit price∂p(xj∗ ,ξj∗ )

    ∂xj,k. The random coefficients for this household i is

    calculated as:

    β̂i,k = α̂j∗,kxj∗,k (12)

    That is, we obtain a random coefficient for every characteristic k and for every household i.

    6.3 Third Step: Finding the Joint Distribution of Preferences and


    We model the relationship between preferences and demographics using a linear model. Denot-

    ing di,s as the demographic characteristic s = 1, ..., S of household i, we can estimate:

    β̂i,k = θ0,k + θk,1di,1 + · · ·+ θk,Sdi,S + ηi,k (13)

    Unfortunately, we do not have observations on the household’s characteristics di,s. Instead, we

    observe the average characteristics of households in each census area dt,s for t = 1, ..., T . We

    follow Bajari and Kahn (2008) and estimate (13) with the group-mean method. We divide the

    i = 1, ..., I households into G groups each of size n = I/G, and write (13) as:

    β̄g,k = θ0,k + θk,1d̄g,1 + · · ·+ θk,S d̄g,S + η̄g,k (14)


  • Table 4: Summary of Implicit Hedonic PricesVariable Mean Std. Dev. 25% 50% 75%Constant 1385.5 95885.4 -59069.1 -14094.1 37535.9Floor 675.1 62.6 642.2 661.7 691.4Net Gross Ratio (%) 1274.3 219.4 1167.4 1253.6 1365.7Gross Area (sq. ft.) 382.1 12.0 375.3 380.5 386.2Bay Window (sq. ft.) -290.2 95.7 -317.8 -294.9 -265.6Age of Structure -1603.6 146.3 -1682.7 -1639.2 -1570.6Swimming Pool 36727.7 4095.9 34880.2 35960.6 37460.1Const. Area Gini -73166.5 32404.9 -84151.0 -69586.5 -57862.5Const. Area % Public Housing -45505.7 6781.4 -48533.5 -46541.0 -44296.8

    That is, we regress the mean preference parameter in each group on the mean demographic char-

    acteristics of each group. We do not observe these group means either, but we can approximate

    it by:

    d̄g,s '1




    dt,s × 1 {t(i) = t} (15)

    The approximation would be close if T and n are large. First, we draw without replacement

    and group the households into G groups each with n members. Next, we calculate the group

    average preference β̄g,k and average demographics d̄g,s by (15). Third, with the G observations

    on β̄g,k and the G observations on each d̄g,s, we can can estimate θ0,k, ..., θk,S for each preference

    parameter k by OLS.

    In Bajari and Kahn (2008) only one draw is made and the OLS standard errors are used

    for inference. To account for the uncertainty in using group means instead of household-

    level demographic characteristics, we draw with replacement and estimate (14) for 1000 times.

    Instead of using the OLS standard errors, we take the standard deviation of the 1000 sets of

    θ0,k, ..., θk,S estimates to build our confidence intervals.

    7 Results and Discussion

    7.1 Hedonic Pricing Estimates

    In Table 4, we show the results of the first step estimation, hedonic prices for various housing

    attributes. Since we use a nonparametric regression technique, we display the distribution of the

    hedonic prices. Most of the average hedonic prices have signs and magnitudes consistent with


  • economic intuition. One floor higher is priced at HK$675.1 per year. Homeowners would pay,

    on average, HK$382.1 per year for each extra square foot in gross area and HK$1274.3 per year

    for each percent increase in the net gross ratio. That is, holding the gross area constant, if we

    increase the net area (for which the home buyer cares more than, say, a bigger swimming pool).

    Of the community characteristics, home buyers prefer a homogenous neighborhood. Home price

    drops, on average, by HK$7,317 when Gini increases by 0.1. In other words, homeowners, on

    average, are willing to exchange 19 square feet of gross area (about the size of a usual bathroom in

    Hong Kong) for a decrease in Gini coefficient in the neighborhood by 0.1. Local income equality

    is a statistically and economically important factor to an average home buyer. In addition, the

    price of each 1% decrease in the people living in public housing is HK$455. Home price can

    drop with more public housing in the constituency area for many reasons: more crime, more

    traffic or higher population density. Whatever the reason, the presence of this characteristic in

    the hedonic price function makes sure that the Gini coefficient variable is not measuring any

    unpleasant effects of public housing, but purely reflecting income distribution.

    7.2 Preferences Estimates

    In the second step of our third-stage estimation, we use the hedonic price estimates, and his

    optimal consumption of various housing attributes, to recover his marginal valuation for various

    housing attributes. In Table 5, we present the distribution of estimates of willingness to pay

    for a 10% increase in consumption of various attributes. In particular, suppose household i’s

    current consumption of attribute k is xk, the willingness to pay for an extra 10% for attribute

    k is:

    WTPi,k = βi,k(log(1.1xk)− log(xk)) = βi,k log(1.1) (16)

    Again, most of the estimates have signs and magnitudes consistent with economic intuition.

    The average homeowner is willing to pay HK$1,197 per year for home that is 10% higher in

    floor, HK$26,348 per year for for a 10% increase in gross area and HK$9,524 per year for a 10%

    increase in the net gross ratio. Homeowners are very sensitive to the age of homes. They are,

    on average, willing to pay almost HK$2,075 less per year for their homes if they are 10% older.


  • Table 5: Consumer Willingness to Pay for Housing AttributesVariable Mean 25% 50% 75%Floor 1197.1 542.5 1049.2 1670.6Net Gross Ratio (%) 9524.0 8644.6 9337.4 10302.2Gross Area (sq. ft.) 26347.8 19685.8 24120.0 29959.6Bay Window (sq. ft.) -599.3 -903.3 -658.4 -225.2Age of Structure -2075.4 -2994.7 -2049.2 -1023.0Swimming Pool 2784.6 3214.6.0 3387.9 3542.2Const. Area Gini -3203.6 -3704.7 -3015.0 -2500.5Const. Area % Public Housing -205.1 0.0 0.0 0.0Units are in HK dollars per year.

    A more homogenous neighborhood is more preferred. The average homeowner is willing to pay

    HK$3,204 to avoid the Gini coefficient in the constituency area to increase by 10%. Again, the

    Gini coefficient is an important consideration for a home buyer: each 1% increase in the Gini

    coefficient is equivalent to a 1.25% decrease in the size of the housing unit. For example, the

    home buyer is indifferent between the Gini coefficient going down from 0.50 to 0.45 and the size

    going up from 1000 square feet to 1012.5 square feet.

    Figure 3 plots the first stage coefficients of Gini on the rental price. If we take rental price of

    the housing unit as a proxy of the buyer’s wealth, Figure 3 shows that richer household dislikes

    income inequality more than less rich household. The third stage estimation described above

    can enable us to quantify this.

    In the third stage estimation, we include four demographic variables in the regression (13):

    • age;

    • household income (’000);

    • marital status (dummies for married, widowed, and separated, and single is the omitted

    group); and

    • education (dummies for less than high secondary, more than high secondary but less than

    college, and college or above, and high secondary is the omitted group).4

    For these variables, we exclude the data of people living in public rental housing, who are

    not homeowners. We then calculate the mean of these variables to be the control variables. In

    4High secondary means completing Form 5, the level at which a student is about 17 years old. This is roughlyequivalent to finishing high school in the US.


  • Figure 3:

    Scatter Plot of Coefficients of Gini and RPrice


  • Table 6: Willingness to Pay for Income Inequality as a Function of Household DemographicsAge 62.8 (38.4)Household Income (in $1,000s) -39.2 (7.0)% Less than High Secondary Education -90.6 (23.9)% Above High Secondary Education -54.6 (35.2)% College or Above -42.2 (19.8)% Married 35.5 (23.8)% Widowed 20.2 (67.9)% Divorced 23.5 (73.3)% Separated -192.1 (185.1)Constant -1039.5 (2500.2)Mean R2– 0.1268

    the calculation of mean age for each constituency area, we exclude certain age groups which are

    not likely to purchase an apartment. In particular, we exclude people under age of 25. Results

    are in Table 6. First, Homeowners with higher income dislikes income inequality more. For each

    HK$1,000 increase of income the the willingness to pay for a 10% increases in Gini goes down

    by HK$40 per year. Second, older homeowners have a higher tolerance for income inequality.

    One year increase in age increases the willingness to pay for a 10% higher Gini by HK$62.8

    per year. While the distribution of the willingness to pay is weakly related to marital status,

    it is strongly related to education level. Comparing to the omitted high secondary education

    group, the lowest education group is much more willing to pay for reducing inequality. For each

    1% increase in the % with less than high secondary education, the willingness to pay for a 10%

    higher Gini increases by HK$90.6 per year. The same holds for the two higher education groups,

    but by a much smaller amount.

    8 Counterfactuals

    In previous sections, we show that homeowners have a strong and statistically significant distaste

    for income inequality in their neighborhood. At the same time, income inequality in some

    neighborhood is made higher due to the existence of public rental housing. In our data, out

    of the 89,090 homes transacted between 2005-06, 27,738 of them are located in constituency

    areas in which there are public rental housing. One natural question to ask is thus: If the Hong

    Kong government separate private and public housing completely, so that private homeowners

    do not have public rental housing in their neighborhood, what would be the welfare gain for


  • homeowners?

    To answer this question, we do the following counterfactual experiment. We propose the

    Hong Kong government to reallocate the poorest 50% public rental housing units to constituency

    areas exclusive to public rental housing. At the same time, we leave the location of homeowners

    unchanged. This can improve welfare of homeowners through two channels. First, Gini coeffi-

    cients in some constituency areas decrease. In particular, out of the 199 constituency areas in

    which we have property transaction data, income inequality in 79 constituency areas changes

    under this policy. Second, the percentage of public housing units in those 79 constituency area

    would drop by 50%.

    Since most transactions (61,456) took place in constituency areas in which this policy has

    no effect, the welfare of these homeowners are not affected by this policy. For the rest of the

    homeowners (27,738), the average welfare gain improves HK$8,126 per year, in which HK$2,150

    is due to lower Gini in those constituency areas and HK$5,976 is due to 50% of public housing

    units in those constituency areas.5

    Is HK$8,126 per year a large amount? We can get an idea of the magnitude by using our

    results in Table 5. The amount of welfare gain is roughly equivalent to increasing the housing

    unit by 20 square feet or having a housing unit 5 years newer. The effect is quantitatively


    9 Conclusion

    People dislike living near others that have a lower or higher income level, and the dislike is

    substantial: on average, a homeowner is willing to pay about HK$3,200 for a 10% drop of

    the local Gini coefficient, which is the amount the home buyer is willing to pay for a 1.25%

    increase in the size of the housing unit. We also find that the dislike of income inequality varies

    with demographics. It goes up with income and is higher with the low education group. A

    counterfactual experiment show that relocating part of the Public Rental Housing improves

    home buyers’ welfare. Of course, the experiment ignores the potential problems of grouping all

    low-income individuals in one area.

    5We have done the experiment for reducing public housing by 75%, and the welfare change is about HK$12000.


  • Our results are local, and we ignore how income distribution is endogenously formed in each

    constituency area. But this paper has identified a large dislike of local income inequality among

    homeowners which deserves further research. Why do home buyers dislike income inequality,

    even after (through the fixed effects) controlling for crime, school quality, and the presence

    of public housing? How should public housing policy be made by taking into account such a

    preference? How does this preference affect local income distribution over time?


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